Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology

Area of Science:

• Computational Science and Engineering
• Artificial Intelligence
• Biomedical Engineering

Background:

• Scientific Machine Learning (ML) is emerging as an efficient alternative to traditional physics-based numerical solvers.
• Current ML approaches build surrogate models for Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs).
• There is a need for advanced ML models capable of handling multiscale, multiphysics problems on complex geometries.

Purpose of the Study:

• To introduce Liquid Fourier LDNets (LFLDNets) as an extension of Latent Dynamics Networks (LDNets).
• To develop parameterized space-time surrogate models for highly nonlinear differential equations.
• To evaluate LFLDNets' performance in computational cardiology applications.

Main Methods:

• LFLDNets utilize a neurologically-inspired, sparse, liquid neural network for temporal dynamics.
• A Fourier embedding with a tunable kernel is employed for improved learning of high-frequency functions.
• The models are applied to 3D test cases in cardiac electrophysiology and cardiovascular hemodynamics.

Main Results:

• LFLDNets demonstrate superior performance in terms of tunable parameters, accuracy, and efficiency compared to neural ODEs.
• The models effectively capture complex spatio-temporal dynamics and high-frequency functions.
• AI-based numerical simulations were executed in minutes on GPUs.

Conclusions:

• LFLDNets provide a powerful and efficient tool for creating surrogate models of complex differential equations.
• This advancement facilitates the development of physics-informed digital twins.
• The approach shows significant promise for applications in computational cardiology and beyond.